Mechanical Reliability

Carnegie Mellon University
18-849b Dependable Embedded Systems
Spring 1998
Authors: Chris Inacio


Embedded systems are complex designs often involving many disciplines in order to create achieve the market demands of price, performance, reliability, and functionality.  As part of this multi-disciplinary design, the reliability of the mechanical components must be taken into account for most of the systems market objectives.  Mechanical reliability has its foundations based in material science, tribology, and deformation mechanics.  Further, understanding of statistics and probability is paramount to understanding and creating a reliable mechanical system.  While the statistics and probability are discussed elsewhere, introductory materials on tribology and some material science are introduced.  Also covered here are precompiled data sources and data modeling techniques relevant to mechanical reliability.

Related Topics:



Mechanical reliability is a very old subject, for as long as man has built things, he has wanted to make them as reliable as possible.  It has been possible in the past to make reliable mechanical systems by simply over engineering them by large factors in order to avoid knowledge of the materials, modes of failure, and other factors which cause mechanical systems to fail.

Today, mechanical reliability is a vastly different topic then when man first started to build structures like bridges and houses.  The study and practice of mechanical reliability is a diversified field.  Research today is often based in material science or tribology (the study of lubricants and wear or fatigue.)  The material science knowledge has greatly advanced the state of the art in mechanical reliability, especially in the past fifty years.  The combination of advanced materials and the statistical modeling of components has lead to a stratified approach to predicting the reliability of mechanical components.

Many standard mechanical components, ball bearings, roller bearings, guide pins, control valves, etc. can be well predicted using historical data.  Many producers of standard components along with the military have generated large databases of stresses, parts, and the the corresponding reliability data for standard parts.  The availability of this data, while generally conservative since the science of building of the components is advancing faster than the historical data gets revised, is a valuable tool in estimating the reliability of standard components.  While standard components have large amounts of historical data which aides in predicting their reliability, predicting the reliability of custom components is less precise.

Mechanical components which are design and fabricated for a specific system cannot easily have their reliability predicted.  The variables effecting the reliability include manufacturing variance, material variance, and applied stress, to name a few.  There are some models developed in order to predict the reliability of these components, but nothing is as accurate as knowing the history of a specific item being used in the specified system.

Part of generating the valuable historical data to predict future reliability of mechanical components is classifying their failure.  The Reliability Analysis Center (RAC) developed a classification for the failure of mechanical components which includes the cause, mode, and mechanism.  This data, while useful for predicting future reliability is also useful for developing regular maintenance schedules and improving the design of similar systems.

Key Concepts

Mechanical failure is classified by three different properties, which together serve to describe a failure in complete detail.  The three key classifications of mechanical failure are the mechanisms, cause, and mode.
These three items combine to give the engineer a key view in understanding how and why a part failed and what can be done to prevent a failure in the future.  It is imperative to understand that mechanical parts, like most other items, do not survive indefinitely without maintenance.  A large portion of mechanical reliability is determining when maintenance should be done in order to prevent a failure.

Available tools, techniques, and metrics


Mechanical engineering is a very old practice.  Man has desired to make mechanical devices for ages.  In man's pursuit of building tools, he has refined the art and craft of designing mechanical tools.  Today, there are various tools available for mechanical engineers.  Systems, such as finite element analysis are very powerful.  In addition, the technology to test mechanical components is impressive.  In man's long pursuit of building mechanical tools, he has developed an advanced and  complex set of mature tools, including simulation and testing to aide in the design process.


The best metrics, for standard or custom components, is historical data of that component in the system in which it will be used.  For example, the best data on when the maintenance for a roller bearing in a conveyer line should be replaced, is knowing when the roller bearings in the same conveyer line needed replacing previously.  Obviously, for new systems, this is not possible.  If the new system is similar enough to a system that the designer has the reliability data, that data should be used.  For completely new systems, however, alternative means of estimating reliability must be employed.

Many standard components have a long history in mechanical engineering.  These standard components are used in many machines in many places without any customization.  Such components, like ball bearings, are available from a multitude of vendors.  Since the use of these components is so wide spread, it makes sense to maintain reliability information on them.  The following table contains a list of references with information that may be applicable to various standard mechanical components.
Data Source Title Publisher and Date
GIDEP Government Industry Data Exchange Program United States Department of Commerce
NPRD-3 Nonelectronic Parts Reliability Data Reliability Analysis Center, RAC, New York, 1985
AVCO Failure Rates D. R. Earles, AVCO Corp., 1962
CCPS Guidelines for Process Equipment Reliability American Institute of Chemical Engineers, 1990
Davenport and Warwick A further Study of Pressure Vessels in the UK 1983-1988 AEA Technology - Safety and Reliability Directorate, 1991
DEFSTAN 0041, Part 3 MOD Practices and Procedures for Reliability and Maintainability, Part 3, Reliability Prediction Ministry of Defense, 1983
R. F. de la Mare Pipeline Reliability; report 80-0572 Det Norske Veritas/Bradford University, 1980
Dexter and Perkins Component Failure Rate Data with Potential Applicability to a Nuclear Fuel Reprocessing Plant, report DP-1633 E. I. Du Pont de Nemours and Company, USA, 1982
EIREDA European Industry Reliability Data Handbook, Vol. 1 Electrical Power Plants EUORSTAT, Paris, 1991
ENI Data Book ENI Reliability Data Bank - Component Reliability Handbook Ente Nazionale Indocarburi (ENI), Milan, 1982
Green and Bourne Reliability Technology Wiley Interscience, London, 1972
IAEA TECDOC 478 Component Reliability Data for Use in Probabilistic Safety Assessment International Atomic Energy Agency, Vienna, 1998
IEEE Std 500-1984 IEEE Guide to the Collection and Presentation of electrical, Electronic Sensing Component and Mechanical Equipment Reliability Data for Nuclear Power Generating Stations Institution of Electrical and Electronic Engineers, New York, 1983
F. P. Lees Loss Prevention in the Process Indestries Butterworth, London 1980
MIL - HDBK 217E Military Handbook - Reliability Prediction of Electronic Equipment, Issue E US Department of Defense, 1986
OREDA 84 Offshore Reliability Data (OERDA) Handbook OERDA, Hovik, Norway, 1984
OREDA 92 Offshore Reliability Data, 2nd Edition DnV Technica, Norway, 1992
RKS/SKI 85-25 Reliability Data Book for Components in Swedish Nuclear Power Plants RKS - Nuclear Safety Board of the Swedish Utilities and SKI - Swedish Nuclear Power Inspectorate, 1987
H. A. Rothbart Mechanical Design and Systems Handbook McGraw-Hill, 1964
D. J. Smith Reliability and Maintainability in Perspective Macmillan, London, 1985
Smith and Warwick A Survey of Defects in Pressure Vessels in the UK (1962 - 1978) and its Relevance to Primary Circuits, report SRD R203 AEA Technology - Safety and Reliability Directorate, 1981
WASH 1400 Reactor Safety Study. An Assessment of Accident Risks an US Commercial Nuclear Power Plants, Appendix III, Failure Data US Atomic Energy Commission, 1974
Data Sources for Part Reliability
Comparing the first three in the table leads to some interesting results.  GIDEP contains data that is submitted by the manufacturers and it is not uncommon for components, specified almost exactly the same to vary in failures rates by many orders of magnitude.  Unfortunately, the US government does not have the resources to regulate the data entered into the database.  GIDEP is, however, very useful for getting a rough estimate of reliability early in the design process.  NPRD-3 reliability data is taken from actual usage of those components in military equipment.  For this reason, the data in the NPRD-3 is very good, however, all of the data is listed as failures per million hours.  Unfortunately, for cyclical equipment, this is a very poor measure.  The appropriate term for cyclical equipment would be in failures per million cycles.  Lastly, the AVCO data contains failure data information for usage in various environments.  Failure for various components can vary greatly depending on the environment in which they are used.  The problem with the AVCO data is that it is from 1962.  Technology, especially materials technology in this case, have advanced tremendously since 1962.

While none of the data sources provides the perfect data for use.  The data contained in the various generic sources may not be perfect, however, it is still very useful for creating new designs.  In order to estimate the reliability of a new mechanical design, it is necessary to use some estimates.  Generally, the estimates given for the generic data is conservative enough that it can be used safely without concern that the device will fail significantly more than estimated.  The downside to the conservative data is that it may cause the designer to increase cost in order to increase reliability.

One could capture just failure rate data for custom mechanical components.  There, is, of course, much more information that can be captured and used to improve both the maintenance and future designs of the system.  It is common in engineering, especially in reliability engineering to quantify and classify failures of systems; unfortunately, the terminology is not the same.  For classifying mechanical failures we will be using the RAC terminology.  The failures are categorized into three fields, the mechanism of failure, the cause of failure, and the mode of failure.

Mechanisms of Failure

The cause of failure can be something as simple as a loss of lubrication.  The mode of failure is the result of the failure mechanism.  An example classification of a mechanical failure is a roller bearing that experiences distortion, (the mechanism of failure,) due to a loss of lubrication, (the cause of the failure,) and caused excessive vibration, (the mode of failure.)  The mode of failure can be used as an aide in diagnosis of system failures.  Further, there are two insights which can can be gained by classifying failures for the design engineer: the practicing engineer can gain a deeper understanding of the stresses present in a mechanical system; secondly, by classifying mechanical failures, an engineer can understand better which analyses need to be done in order to better predict the reliability of the component in its environment.


A simple example of using generic data to estimate the reliability and determine the probability for a system to complete its mission follows.  This example is completely fictional and from [Ireson].
Part Description Quantity Cyclic Use General failure rate per million hours Total failure rate per million hours Data Source
Heavy-duty ball bearing 6 N/A 14.4 86.4 AVCO
Brake assembly 4 N/A 16.8 67.2 AVCO
Cam 2 1 h-1 0.016 0.032 AVCO
Pneumatic hose 1 N/A 29.28 29.28 AVCO
Fixed displacement pump 1 N/A 1.464 1.464 NPRD-3
Manifold 1 N/A 8.80 8.80 AVCO
Guide pin 5 N/A 13.0 65.0 AVCO
Control valve 1 40 h-1 15.20 15.20 AVCO
Total assembly failure rate 273.376
If the mission time for this assembly is 500 hours, the probability of success would be:
Ps = e(-500 x .000273376) = .872.  This value is probably pessimistic considering that much of the data is from AVCO, however, it does provide a good starting point.  Further, if any single component is extremely critical, it is strongly recommended that an in depth stress strength analysis is performed on that component.

Models of Mechanical Failure

Two of the more accurate models of mechanical failure are the maximum normal stree theory and the distortion energy theory. [SADLON93]  These models rely on the design engineer being able to predict the level of stress that will be applied to a component in order to estimate its reliability.  By using these models, first proposed at the turn of the 20th century, an engineer can accurately estimate the reliability of the component.  Unfortunately, both of these methods requires a significant amount of time, and if a generic data source can estimate that a component will not fail within the mission time of the system with an acceptable high probability and the component is not generally safety critical, then this analysis can be avoided.

Maximum Normal Stress Theory

The maximum normal stress theory was first proposed by Rankine and is also known as Rankine's theory of failure. [SALDON93]  The maximum normal stress theory is particularly well suited to materials that are brittle as opposed to ductile materials.  For example, materials such as cast iron are well suited to this method while materials such as urethane foam are not.  Rankine's summary of this theory is that "failure is predicted to occur in the multi-axial state of stress when the meximum principal normal stress becomes equal to or exceeds the maximum normal stress at the time of failure in a simple uniaxial stress test using a specimen of the same material."  This means that a sample of the same material, cast iron for instance, is taken to a lab, and the iron is tested for its maximum stress amounts.  In order to do the testing, both tensile, pulling, and compressive, squeezing, forces are applied to the material in one axis only.  When an engineer wants to determine wether a part will fail or not, he can take multiaxial stress, create the normal force vectors, and see if any of the normalized force vectors exceeds the capability of the material.  If a normalized stress does exceed the capability of the material, the material is predicted to fail.

Distortion Energy Theory

Relationship to other topics

Traditional Reliability

In order to understand mechanical reliability, it is necessary to understand traditional reliability.  The math behind calculating reliabilities is the same.  Furthermore, techniques, including parallel and serial reliability are fully explained.

Electronic Reliability

Traditional electronic reliability uses many of the same concepts of diversity and redundancy in order to achieve reliability and fault tolerance.  There are many parallels between the two disciplines.  There are however, many differences.  Mechanical parts wear due to corrosion, friction, and other mechanical stresses.  Electrical components do not wear in the same manner, and so preparing for wear in the design phase is very different.  Electrical components experience drift, which the the designer must make design accomodations.  The effect of the different types of wear are different approaches to maintenance.  The mechanical maintenance program may involve replacing parts that wear, while the electrical approach may involve using feedback mechanisms and calibrating the electronics to account of electrical wear, or drift.


Mechanical reliability is a very old craft practiced for more than a century.  The sciene behind mechanical reliability is constantly improving with better lubricants and materials beign researched and created.  The methods to estimate and produce reliable mechanical components exist.  Using the existing tools and methods, extremely reliable mechanical systems can be created.  Just like in most forms of reliability, using diversity and replication can create fault tolerant systems for safety critical systems.

Annotated Reference List

Loose Ends

I need to complete the section on the distortion energy theory, I require getting a more original source, instead of quoting quotes.

Go To Project Page